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Definite integrals properties review

Review the definite integral properties and use them to solve problems.

What are the definite integral properties?

Sum/Difference: ab[f(x)±g(x)]dx=abf(x)dx±abg(x)dx
Want to learn more about this property? Check out this video.
Constant multiple: abkf(x)dx=kabf(x)dx
Want to learn more about this property? Check out this video.
Reverse interval: abf(x)dx=baf(x)dx
Want to learn more about this property? Check out this video.
Zero-length interval: aaf(x)dx=0
Want to learn more about this property? Check out this video.
Adding intervals: abf(x)dx+bcf(x)dx=acf(x)dx
Want to learn more about this property? Check out this video.

Practice set 1: Using the properties graphically

Problem 1.1
20f(x)dx+03f(x)dx=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
units2

Want to try more problems like this? Check out this exercise.

Practice set 2: Using the properties algebraically

Problem 2.1
13f(x)dx=2
13g(x)dx=5
13(3f(x)2g(x))dx=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Want to try more problems like this? Check out this exercise.

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